On interpreting Gödel's Second Theorem

Summary In this paper I have considered various attempts to attribute significance to G2.²⁵ Two of these attempts (Beth-Cohen and the position maintaining that G2 shows the failure of Hilbert's Program), I have argued, are literally false. Two others (BCR and Resnik's Interpretation), I have argued, are groundless.I would like to thank Dale Gottlieb, Stephen Barker, Tim McCarthy, Philip Kitcher, Michael Resnik and Richmond Thomason for extensive and helpful discussion of this work.     

Reinforcement magnitude and the inhibiting effect of reinforcement

In a two-key concurrent variable-interval schedule (using pigeons), if the reinforcement frequency for one response is held constant while that for the other is increased, the rate of response on the constant key decreases. The immediate reinforcement for key pecking can usually be conceptualized as the change from a condition in which the key light is on and the food hopper light is off to one in which the key light is off and the hopper light is on. The prechange condition is associated with a delay to food of one-half the average interreinforcement interval in effect during this condition. The postchange condition is associated with a delay to food of about .5 seconds. The programming of additional reinforcement results in a decrease in the delay to food associated with the prechange stimulus condition, and thus a decrease in the value of the improvement that results from the change. This would appear to be analogous to a decrease in the amount of reinforcement, and thus sufficient explanation for the decrease in the rate of the response.     

Relevant Robinson's arithmetic

In this paper two different formulations of Robinson's arithmetic based on relevant logic are examined. The formulation based on the natural numbers (including zero) is shown to collapse into classical Robinson's arithmetic, whereas the one based on the positive integers (excluding zero) is shown not to similarly collapse. Relations of these two formulations to R. K. Meyer's system R# of relevant Peano arithmetic are examined, and some remarks are made about the role of constant functions (e.g., multiplication by zero) in relevant arithmetic.This paper has been greatly influenced by the (largely unpublished) work of E. K. Meyer (cf. [7]) on relevant arithmetic, and I wish to thank him, and also N. D. Belnap, Jr. and D. Cohen for helpful advice. In fairness to Meyer it must be said that he finds my axioms 13 and 13(1) too strong (they are not theorems of his system R# - cf. §4 below). Meyer tells me be finds vindication for his view in my chief theorem of §2. For myself, I find the insights behind Meyer's work on R# to be both stable and fruitful, and if I now had to make a choice, I would follow Meyer in his rejection of my axioms. However, the systems I explore in this paper themselves have a surprising amount of internal consistency of motivation (cf. §5). Let a hundred formal systems bloom.     

A theorem in 3-valued model theory with connections to number theory,type theory,and relevant logic

Given classical (2 valued) structures and and a homomorphism h of onto , it is shown how to construct a (non-degenerate) 3-valued counterpart of . Classical sentences that are true in are non-false in . Applications to number theory and type theory (with axiom of infinity) produce finite 3-valued models in which all classically true sentences of these theories are non-false. Connections to relevant logic give absolute consistency proofs for versions of these theories formulated in relevant logic (the proof for number theory was obtained earlier by R. K. Meyer and suggested the present abstract development).     

The role of some definite references in linguistic integration

Definite reference increases thematic integration for semantically related sentences (DeVilliers, 1974). Therefore, definite reference should increase linguistic integration in the Bransford-Franks integrated recognition paradigm. Two recognition and two recall studies demonstrated that, if anything, indefinite reference increases linguistic integration effects, as measured by existing measures of integration. However, definite reference increases topical clustering in recall. Results cast doubt on the validity of existing measures of linguistic integration and indicate that the tally model of performance in integrated recognition tasks (Reitman & Bower, 1973) is not totally adequate, either. Results are compatible with the associative model of Anderson and Bower (1973). Topical clustering appears to be a better measure of integrated memory than are existing measures of linguistic integration. Retention of information about the propositional form in which semantically related sentences are presented and integrated memory are not necessarily incompatible.     

Response and encoding factors in “ignoring” irrelevant information

Subjects classified either the numerosity or numeric value of elements in successive stimulus displays. In separate experiments, responses were indicated by oral naming, card sorting, manual tapping, and oral “tapping.” Incongruent levels of numeric value slowed naming and sorting, but not tapping, when numerosity was the cue for responding. Incongruent numerosity slowed tapping, but not naming and sorting, when numeric value was the cue. Changes in stimulus response mapping may thus critically alter the ability to ignore an irrelevant stimulus dimension.     

Values of British political extremists and potential extremists: A discriminant analysis

Studied the value systems of political extremists and potential extremists, comparing them with the value systems of centrist activists and supporters. Samples of political activists from the Labour, Conservative, Communist and National Front parties were obtained, as well as samples of non-active supporters. The non-active supporters were defined as Potential Extremists, if they supported a centrist party as first choice, but either Communist or National Front as second choice. All subjects completed the Rokeach Value Survey. Discriminant analysis showed that the four groups of activists could be clearly distinguished on the bask of their values. However the values of the Potential Extremists did not especially resemble the values of actual National Front or Communist activists. There were value differences between the Potential Extremists and the centrist supporters; nevertheless these two groups tended to be distinguished by very different values from those which distinguished between the activists. The appeal of value symbols for different types of political involvement was discussed.     

Cognitive,social, and other correlates of specific reading retardation

Children with specific reading retardation were matched with controls on the basis of age, sex, intelligence, and (less successfully) parental education. All subjects were tested on a variety of automated performance tests including the Matching Familiar Figures (MFF) Task, Auditory-Visual Integration, Short-Term Memory, the Continuous Performance Task (CPT), and Motor Performance. All children were assessed socially using the Conners Teacher Questionnaire, and reading-retarded children were rated on the Behavior Problem Checklist. Finally, all children were screened with the Finger Twitch Test and were assessed for left-right awareness. Statistical analysis suggested that the following performance tests discriminated between the groups in this respective order of importance: MFF (Accuracy), Auditory-Visual Integration, and the CPT. The Short-Term Memory Task, MFF Decision Time, and Motor Performance did not distinguish between the groups. Multiple regression equations suggested that scores on the performance tests could account for about 40% of the variance in reading attainment. Several factors from the rating scales (notably those pertaining to attention and anxiety) and left-right awareness also discriminated between the groups.This study was supported by a grant from the Medical Research Council of New Zealand to Prof. J. S. Werry (Grant MRC 151). The author would especially like to thank John Werry, M. D., Malcolm Gill, Ph.D., and the staffs of the official Remedial Reading Clinics and Psychological Services as well as those of Epsom Normal, Mount Eden Normal, Newmarket, and Parnell primary schools for the willing support they all rendered this project.     

Hairdressers as caregivers. I. A descriptive profile of interpersonal help-giving involvements

The interpersonal help-giving behaviors of 90 hairdressers were explored in depth in an interview study. On the average, hairdressers saw 55 customers a week, and talked 25 minutes with each. About one-third of the talking time concerned clients' moderate to serious personal problems--particularly problems with children, physical health, marriage, depression, and anxiety. Hairdressers reported that offering sympathy and support, being lighthearted, just listening, and presenting alternatives were among their most frequent response strategies. Although they often enjoyed fielding clients' personal problems, at times they felt perplexed by them. Hairdressers perceived listening to customers' interpersonal problems to be an important part of their everyday function and expressed a need for professional inputs in that domain.